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26 Aug 2010, 23:14
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B
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When positive integer m is divided by positive integer n, the remainder is 12. If m/n = 24.2, what is the value of n ?
(A) 120
(B) 60
(C) 30
(D) 24
(E) 12
(A) 120
(B) 60
(C) 30
(D) 24
(E) 12
whiplash2411
Joined: 09 Jun 2010
Last visit: 02 Mar 2015
Posts: 1,761
Given Kudos: 210
Status:Three Down.
Concentration: General Management, Nonprofit
Schools: HBS '17 (M) Stanford '17 (A)
26 Aug 2010, 23:22
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Okay so when you're given that the remainder is 12 you can rephrase it as:
m = k*n + 12 where k is the quotient.
But we are given that m = 24.2n.
The quotient in the first part is a whole number, and hence k = 24. We can assume this because the decimal part in the second statement given to us, i.e the 0.2 corresponds to the remainder. We get the decimal since the remainder is smaller than the divisor.
So if we substitute the value of k into this equation, we get:
\(24.2n = 24*n + 12\)
\(0.2 n = 12\)
\(n = \frac{12}{0.2} = 60\)
So the answer is B.
m = k*n + 12 where k is the quotient.
But we are given that m = 24.2n.
The quotient in the first part is a whole number, and hence k = 24. We can assume this because the decimal part in the second statement given to us, i.e the 0.2 corresponds to the remainder. We get the decimal since the remainder is smaller than the divisor.
So if we substitute the value of k into this equation, we get:
\(24.2n = 24*n + 12\)
\(0.2 n = 12\)
\(n = \frac{12}{0.2} = 60\)
So the answer is B.
21 Mar 2017, 06:11
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zisis
When positive integer m is divided by positive integer n, the remainder is 12. If m/n = 24.2, what is the value of n ?
(A) 120
(B) 60
(C) 30
(D) 24
(E) 12
(A) 120
(B) 60
(C) 30
(D) 24
(E) 12
This problem will be best solved using the remainder formula. Let’s first state the remainder formula:
When positive integer x is divided by positive integer y, if integer Q is the quotient and r (in which 0 ≤ r < y) is the remainder, then x/y = Q + r/y.
In this problem, we are given that when positive integer m is divided by positive integer n, the remainder is 12. So, we can say:
m/n = Q + 12/n
We also are given that m/n = 24.2. Using the remainder formula, we can say:
m/n = 24.2
m/n = 24 + 0.2
m/n = 24 + 2/10
m/n = 24 + 1/5
Because Q is always an integer, we see that Q must be 24, and thus the remainder 12/n must be 1/5. We can now equate 12/n to 1/5 and determine the value of n.
12/n = 1/5
n = 60
Answer: B
